【摘要】 以特殊的线性振荡方程y″+g(t)y=0(其中limt→∞g(t)=+∞)为例讨论了高振荡微分方程数值解的问题.分析了梯形格式的整体截断误差,并对梯形格式做了修改,讨论了修改后格式的局部截断误差对整体截断误差的影响,最后给出了数值结果.更多还原

【Abstract】 This paper deals with numerical solutions of highly-oscillatory ordinary differential equations with a special reference to the linear oscillator y″+g（t）y=0(where lim_t→∞ g（t）=∞).Analyzing the global error,we modified the trapezoidal method.We investigated the influence of the modified local error on the global error.Finally,modified some numerical results were given.更多还原